Tania_Colligan_17818782_Assessment 1 _EDP243_SP2023

docx

School

Curtin University *

*We aren’t endorsed by this school

Course

243

Subject

Computer Science

Date

Jan 9, 2024

Type

docx

Pages

Uploaded by DukeSalmon3192

Tania Colligan 17818782 Assessment 1 Part A – Relational / Conceptual The foundation for all maths concepts is students learning number and place value. It is a starting point for understanding other base systems. When students understand place value base ten, it helps them to regroup and multiply multiple digits (Hartnett, 2018. p 36). An example of a student understanding place value is representing the number 31 with 2 three blocks of 10- and one-unit blocks; however, if they can show the other ways of showing 31, like two blocks of 10 and 11 one-unit blocks, then it is relational understanding (Van de Walle et al., 2019. p 22). Richard Skemp developed the term relational understanding to show the web of representations of maths concepts that link and make connections, which builds relational understanding. It is doing something with knowing why and mastering maths. (Van de Walle et al., 2019. p 22). Relational understanding is developed over time using schemas to assist with it (Hartnett, 2018. p 36). Cognitive schemas are Jean Piaget’s explanation of how students learn using existing ideas to develop new ideas. These then modify to assimilate if it does not exist, then the schema accommodates (Van de Walle et al., 2019. p 27). In contrast to relational understanding, conceptual uses intuitive understanding to connect to new knowledge. It encourages the students to think deeply and flexibly with a web connecting images, concrete materials, and abstract representation (Van de Walle et al., 2019. p 26). An example of this is in Figure 1, which shows four different ways of conceptual variation for the sum 3 x 5 = 15, linking different contexts for that sum ( Conceptual Variation 2020). Conceptual understanding is a process of making errors while developing the concept. Learning is an active process and depending on the Zone of Proximal Development (ZPD), their peers can support their knowledge. Vygotsky believes social learning settings help developmental processes (Hiebert et al., 1997). An activity to help develop a conceptual understanding of place value is to divide into groups of 2 to 3 and give a number for them to expand, show more and less, word form, base ten blocks and what the place value is. It scaffolds their learning by examining different strategies through problem-solving and discussions on their thinking (Van de Walle et al., 2019. p 28). 1 Figure 1 ( Conceptual Variation 2020)

Tania Colligan 17818782 Assessment 1 Part B – Resources Year 2 Counting Large Collections AC9M2N02: partition, rearrange, regroup and rename two- and three-digit numbers using standard and non- standard groupings; recognise the role of a zero digit in place value notation.  comparing the digits of a number with materials grouped into hundreds, tens and ones, and explaining the meaning of each of the digits in the materials. ( V9 Australian curriculum 2022) It is designed for the students to unitise the unifix cubes. An important part of understanding place value is seeing that a group can make a unit. In this activity, the plan is for the students to group 10 unifix cubes and count them as 1 unit. In a group task, the students can learn from each other through sharing and comparing strategies. Using concrete materials helps the students to visualise place value through stacks of 10 as 1 unit and the loose parts as 1 unit. At the end of the lesson, the class teacher would discuss as a class the students’ findings and provide an opportunity for them to share their experiences (reSolve, 2020). Year 3 Show it four ways. AC9M3N0: recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000.  moving materials from one place to another on a place value model to show renaming of numbers; for example, 1574 can be shown as one thousand, 5 hundreds, 7 tens and 4 ones, or as 15 hundreds, 7 tens and 4 ones. ( V9 Australian curriculum 2022) 2 Figure 2 (reSolve, 2020)

Tania Colligan 17818782 Assessment 1 The task is designed to look at place value in various ways and develop an understanding of how to represent numbers. It encourages the mental processes to develop and build on previous understanding of place value. The aim is for students to see the number value and represent it in 4 different ways. It will show if they understand the base-ten number system, which is needed to build and connect to the place value concept. The materials will give a chance to manipulate and work out and experiment to find ways to make the number. Then, the students share their work with the class to show others and explain their representations (Silva, 2005 & Hartnett, 2018). Year 4 Length model We’re going to create decipipes! AC9M4N01 recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals.  using materials to show the multiplicative relationship between the whole, tenths and hundredths; for example, using a bundle of 10 straws to represent the whole, one straw as the tenth and cutting the tenth into 10 parts to show the hundredths; using “Decipipes” to represent tenths. ( V9 Australian curriculum 2022) The task involves students building decipipes and then using them to show decimals. It will encourage language of decimals and fractions, showing a connection that “0.2 is two-tenths” ( Department for Education plink 2021). It is an important activity to continue using precise language to support the students' understanding and link to fractions. For example, they hear two-tenths instead of zero-point two. A misconception can happen with them thinking longer is larger due to the whole number thinking from previous lessons. For example, 0.36 is larger than 0.5 because it has more digits. The decipipe is a linear model that can show the decimals' size for the students to understand decimal numbers. ( Department for Education plink 2021). Part C – Multiplicative Thinking 3 Figure 3 (Silva, 2005) Figure 4 (Department for Education plink 2021)

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Tania Colligan 17818782 Assessment 1 Multiplicative thinking is being able to find relationships with quantities and to share an understanding of the problem. It involves working with numbers in a flexible way using concepts of multiplication, division, fractions, and percentages (Hurst & Hurrell 2016, p 2). Researchers have shown that when students are presented with different ways of solving problems, it enhances their learning rather than overwhelming them; it gives them the flexibility to solve it in various ways (Van de Walle et al., 2019. p 282). Hurst believes that teaching division as multiplication is a way to get out of the addition mode and look at splitting concepts, which would enhance multiplicate thinking and, therefore, would help with concepts in future like fractions. Researchers who were investigating children’s multiplicative thinking discovered two main concepts with multiplicative thinking: equal groups and language of factors and multiples (Hurst & Hurrell 2016, p 2). It has been argued that looking at multiplication through arrays develops a conceptual understanding rather than teaching basic multiplication facts (Hurst & Hurrell 2018, p 24). Arrays help develop the properties of multiplication it shows the “factors are the same so that the product will be the same” (Hurst & Hurrell 2018, p 24). The second concept for multiplicative understanding is the language of factors and multiples; part of it is explaining their ideas and working out. It shows their ability to relate ideas to the communitive property in arrays. When they do this, it builds more of an understanding than memorising a number factor of multiplication. Diagnostic question 1. Year 5 This question is designed to see their manipulative thinking if they can think of a way to work it out without just multiplying eight by 15. If a student showed their working out to break the number up to multiples, they knew, for example, they could break up the number 15 into 10 and 5. Then showed that 8 x 10 = 80 and 8 x 5 = 40. Next, the student looked at 8 + 4 = 12 and added zero, which made the answer 120. The student had sound multiplicative thinking, demonstrating knowledge of multiples of 8. Then, the ability to break fifteen into workable numbers shows the understanding of place value, recognising 10 in the number 15. 4 Figure 5 (Teachers Click,

Tania Colligan 17818782 Assessment 1 Diagnostic question 2. Year 5 This question requires more logical deduction and simplifying the problem while being open to context interpretation. The year five student may need to find strategies for listing, finding a rule, or acting it out to work it out. Posing questions like “How many are needed to ensure two of the same colours?” (Ali’s Beans, Problemo, 2021). A student can initially deduct that there are five colours, divide that into 100, and work out that it is 20. Then, discover that there are 20 of each colour and think they have solved the problem. It would show me they haven’t thought of all the possibilities and not thought of patterns that may occur when picking out the colours. The student did not think about ensuring that a pattern continues to occur the 5 th time one of the colours to ensure that there are 20 of each colour so that the answer will be 21, not 20. Diagnostic question 1 year 6. 5 Figure 5 (Problemo,

Tania Colligan 17818782 Assessment 1 The year six student shows multiplicative understanding and chose A 20. The first work showed how many 25 is in 200, which is 8. So, they presented that eight batches were needed. It demonstrated that they could manipulate and divide 200 into eight and how many 25 is in 200. The student has knowledge of numbers and grouping, which was confirmed by finishing the solving the question by devising to times eight by 2.5 to get the answer 20. It showed a multiplicative understanding of multiplication and division. Diagnostic question 2 year 6. Question 2 will demonstrate knowledge of place value, subtracting, and interpreting the problem. If the student cannot manipulate the numbers around to make the largest and smallest, they need more work on place of hundreds, tens, and ones. Another misconception they show is not changing the 5 and 7 over to make 257, which will be the lowest number. By year six, a strong place-value base ten knowledge should be acquired. However, questions like this would help diagnose and determine if they need work on multiplicative thinking on place value and subtraction. Part D – Learning Activities 6 Figure 6 (Problemo, Figure 7 (Problemo,

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Tania Colligan 17818782 Assessment 1 Domino Arrays Learning intentions To build students’ multiplicative thinking using arrays, whereby all parts of the array are not visible. The sequence encourages students to find the total number of items in an array by multiplication rather than counting by 1s or skip counting. The connection between area, arrays and multiplication is also made. Australian Curriculum: Mathematics (Year 3) ACMNA056: Recall multiplication facts of two, three, five and ten and related division facts. ACMNA057: Represent and solve problems involving multiplication, using efficient mental and written strategies and appropriate digital technologies. (Domino Arrays, Resolve website 2020) Lesson 1: Which Uses the Most? Students explore the number of dominoes required to cover a rectangle. They are presented with four domino designs placed in different orientations. As the students work through the problem, they realise that the same number of dominoes will be used regardless of orientation. Students are then asked to explain why the same number of dominoes is used. (Domino Arrays, Resolve website 2020) The students will be asked to work in groups and can support each other's learning and manipulation of arrays. Using arrays is a way to learn multiplication and allows the student to gain understanding rather than learning in a rote way. For the first lesson, the teacher will give the option to use dominoes or cut-outs to help the students visually see the arrays and support those who require additional help. This would accommodate all needs; those who do not use them can challenge their thinking and understanding, and those who will benefit from having that extra visual support. At the end of the lesson, the teacher regroups as a whole class to discuss each other’s findings and learn of their mathematical reasoning. 7 The actual task for students Example of the task. Prompts to show thinking.

Tania Colligan 17818782 Assessment 1 Make a Statement. Learning intention Students write their own true/false open sentences. The connection to the equal sign is made. Australian Curriculum: Mathematics (Year 3) ACMNA054 Recognise and explain the connection between addition and subtraction  demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences (ACARA, Mathematics 2018) Prior knowledge The students in lesson one worked through true/false statements as a class. Lesson 2 Ask students to write their own true/false and open sentences to challenge their classmates. The students must write three equations with one true and one false sentence. A template can be provided for students who need the structure (Van de Walle et al., 2019. p 332). (Van de Walle et al., 2019. p 332). It enhances their relational thinking through using numbers and is designed for them to understand the equal sign concept. The sum, if it is true, should equal the same answer, for example, 5 +7 = 6 + 6. When the students trade with other students, they have an opportunity to develop and learn from each other, which Vygotsky calls scaffolding their learning. 8

Tania Colligan 17818782 Assessment 1 Part E – Investigation “Multiplication is just repeated addition.” Multiplication is just repeated addition, a state that some teachers may teach students. However, it may be a concept initially taught to younger students when introducing multiplication, but that thinking will not consolidate into other concepts like fractions (Van de Walle et al., 2019. p 185). Hurst states there is a difference between additive thinking and multiplicative; he labelled it as being in the ‘counting world’ and ‘splitting world’. The splitting world works with both multiplication and division together. Because of the focus on the counting world, the research study showed that 52% of the year 5s were not multiplicative thinkers and, therefore, were more focused on addition to solving multiplication (Hurst & Hurrell 2016, p 2). Arrays are a way to build multiplication with a better connection to learning the concept. Students begin to look at arrays in year 2 with ACARA, which develops the notion that the 1st number tells how many sets of groups or arrays there are. The second number gives information on the size of each group. Then, the third number is a sum of both numbers, showing a whole product (Van de Walle et al., 2019. p 185). It is a way that the students can consolidate their understanding and further use it when learning other concepts. (Hurst & Hurrell 2018, p 23). “All children learn mathematics in the same way.” Students need to make connections to make meaning and understand mathematics; therefore, it is an individual thing. They can only move on to the next stage or concept if they understand. (Van de Walle et al., 2019. p 8). Mathematics should provide various hands-on experiences with materials to benefit the students learning. A study Price reported showed that 96% of teachers that using materials helped their student's growth and learning (Hartnett, 2018. p 36). Children do not learn the same way due to the varied experiences that construct their knowledge. So, it would depend on their experiences and the construction of their knowledge. Jean Piaget developed constructivism and believed children develop and construct their own learning (Van de Walle et al., 2019. p 27). Doing maths is an active way of connecting through searching for patterns and analysing problems. It also involves considering peers' solutions (Van de Walle et al., 2019. p 16 -18). Lev Vygotsky believed that learning is a social process and that teachers or other students need scaffolding. When students listen or share their thoughts, it develops knowledge and understanding. The learner has a zone of proximal development (ZPD) and knowledge that is out of reach of the learner and needs support from peers or teachers to help them. (Van de Walle et al., 2019. p 28). 9

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Tania Colligan 17818782 Assessment 1 Reference Australian Curriculum, Assessment and Reporting Authority . (2022). V9 Australian curriculum . Home | V9 Australian Curriculum. https://v9.australiancurriculum.edu.au/ 10

Tania Colligan 17818782 Assessment 1 Domino Arrays. (2020). Resolve website . reSolve. https://www.resolve.edu.au/multiplication-domino-arrays https://neasdenprimary.org.uk/wp-content/uploads/2020/09/Maths-at-Neasden.pdf Figure 1 Concept Variation Hartnett, J. (2018). Teaching place-value: Concept development, big ideas and activities . Department of Education. https://files.eric.ed.gov/fulltext/EJ1231242.pdf Hiebert, J. (1997). Teaching Mathematics for Understanding Chapter 1. In Making Sense: Teaching and Learning Mathematics with Understanding (pp. 1–12). essay, Pearson. Hurst, C. and Hurrell, D. (2016) Investigating Children’s Multiplicative Thinking: Implications for Teaching, European Journal of STEM Education, 1:3 (2016), 56. Hurst, C., & Hurrell, D. (2018). Algorithms are great : What about the mathematics that underpins them? Australian Primary Mathematics Classroom; v.23 n.3 p.22-26; 2018, 23(3), 22–26. https://search.informit.org/doi/10.3316/aeipt.223104 Mathematics . The Australian Curriculum (Version 8.4). (2018). https://australiancurriculum.edu.au/f-10- curriculum/mathematics/?strand=Statistics%2Band %2BProbability&capability=ignore&priority=ignore&year=11754&elaborations=true&cd=ACMNA054&searchT erm=#dimension-content Neasden Primary School. (2020). Conceptual Variation . Maths at Neasden. Retrieved September 29, 2023, from https://neasdenprimary.org.uk/wp-content/uploads/2020/09/Maths-at-Neasden.pdf . Problemo. (2021). Problemo . https://app.problemo.edu.au/problem/771/view Silva, M. (2005). Numeracy Project . Curtin University. https://lms.curtin.edu.au/webapps/blackboard/content/listContent.jsp? course_id=_133274_1&content_id=_11622775_1&mode=reset Teachers Click. (2020, April 29). Diagnostic test (grade 5) . https://www.teachersclick.com/2020/04/diagnostic-test- grade-5-all-subjects.html The Department of Education, the Government of South Australia. (2021). Department for education plink . Department for Education plink. https://www.plink.sa.edu.au/ilp/pages/course.jsf? courseId=12370228&pollingMode=on#!/courseroom/course Van de Walle, J., Karp, K., Bay-Williams, J., Brass, A., Bentley, B., Ferguson, S., Goff, W., Livy, S., Marshman, M., Martin, D., Pearn, C., Prodromou, T., Symons, D., Wilkie, K., & Wray, J. (2019). Primary and middle years mathematics: Teaching developmentally . Pearson Australia. September 11, 2023, https://ebookcentral.proquest.com/lib/curtin/reader.action?docID=5830083# 11

Tania_Colligan_17818782_Assessment 1 _EDP243_SP2023

Related Documents